First, a electrical signal is created from a stimulus. The message is sent from the nucleus in the cell body down through the axon to the axon terminal. Myelin sheaths will speed up the signal as well.
When an impulse is being transmitted, the stimulus is causing the channels to open and Na+ flows in; depolarizing the neuron. Then as the impulse passes, K+ flows back outside which resumes the neuron's polarization.
Then, the signal releases a neurotransmitter which jumps over the synapse to another neuron to pass on the message. That is received by the dendrites of that neuron and passed on through the neurons until the signal reaches its destination.